The long-term objective of the proposed research is development of statistical methods for mapping and genetic analysis of human complex traits, which account for a major portion of the health care burden in the United States. Complex traits are familial, but do not have simple patterns of transmission and are likely to result from the actions and interactions of multiple genetic and environmental factors. With the availability of high-density single-nucleotide polymorphism information, there is the potential to use association-based mapping methods to identify relevant genetic variants, as well as to clarify the role of environmental risk factors. Case-control association tests are more versatile in terms of the study designs they can accommodate than are TDT-type association tests. Most case-control association mapping methods are designed for samples of unrelated individuals, but families containing two or more affected individuals remain a powerful resource for genetic association studies, because under complex genetic models, affected individuals with affected relatives are enriched for disease-predisposing alleles, compared to affected individuals without affected relatives. Thus, these individuals should be expected to contribute disproportionately to the power of a case-control association study. Robust, powerful association mapping methods are needed that will be useful in a full spectrum of study designs, from simple combinations of sibships with unrelated individuals on the one hand, to isolated founder populations with complex inbred pedigrees, on the other hand. Another critical aspect of association testing is the ability to detect and account for violation of assumptions that may cause false positive results, including (1) population stratification and (2) experimental artifacts that may cause artificial case-control differences. Our specific aims include methods development for (1) association mapping in samples that contain arbitrarily related individuals, including robust and powerful methods for both binary and quantitative traits, allowing for haplotype effects, covariate information, effects of multiple loci, and possible interactions among these, where these methods are broadly applicable across a wide range of study designs; (2) association mapping methods that simultaneously adjust for the possible presence of population stratification in the sample by principal components analysis and allow for related individuals in the sample; (3) tests for informative missingness of marker genotypes in the context of association testing, in order to detect possible false positive association results that are due to experimental artifacts.